5 Continuous mappings Flashcards
1
Q
Continuous mapping
A
Let (X, T) and (Y, T1) be topological spaces and f a function from X into Y. Then f: (X, T) -> (Y, T1) is said to be a continous mapping if for each U e T1, f-1(U) e T.
2
Q
Path-connected topological space
A
A topological space (X, T) is said to be path-connected (or pathwise connected) if for each pair of distinct points a and b of X there exists a continuous mapping f: [0,1] -> (X, T) such that f(0) = a and f(1) = b. The mapping f is said to be a path joining a to b.
